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A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

C++ Tutorial

Introduction of C Programming for DSP Applications

Fixed-Point Arithmetic: An Introduction

Cascaded Integrator-Comb (CIC) Filter Introduction


IIR Filter Design Software

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Embedded SystemsFPGA

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Sinusoids and Exponentials

This chapter provides an introduction to sinusoids, exponentials, complex sinusoids, and various associated terminology, such as exponential decay-time ``$ t_{60}$'', in-phase and quadrature sinusoidal components, analytic signals, positive and negative frequencies, and constructive and destructive interference. The fundamental importance of sinusoids in the analysis of linear time-invariant systems is introduced. We also look at circular motion expressed as the vector sum of in-phase and quadrature sinusoidal motions. Both continuous and discrete-time sinusoids are considered. In particular, a sampled complex sinusoid is generated by successive powers of any complex number $ z$.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See for details.


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